改进了半轴上Schrödinger算子的尖锐谱不等式

IF 1 3区数学 Q1 MATHEMATICS

Journal of Spectral Theory Pub Date : 2019-12-31 DOI:10.4171/jst/434

L. Schimmer

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引用次数: 3

摘要

证明了半轴上具有Robin边界条件的Schr\ odinger算子的Lieb—Thirring不等式。该结果改进了P. Exner, a . Laptev和M. Usman [comm]所得到的界。数学。物理学报，2011,31(2):531—541(2014)。在我们的证明中，主要的区别是我们用双换相法代替了单换相法。在狄利克雷边界条件下，我们还建立了一个改进的不等式。

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Improved sharp spectral inequalities for Schrödinger operators on the semi-axis

We prove a Lieb--Thirring inequality for Schr\"odinger operators on the semi-axis with Robin boundary condition at the origin. The result improves on a bound obtained by P. Exner, A. Laptev and M. Usman [Commun. Math. Phys. 362(2), 531--541 (2014)]. The main difference in our proof is that we use the double commutation method in place of the single commutation method. We also establish an improved inequality in the case of a Dirichlet boundary condition.

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来源期刊

Journal of Spectral Theory MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.00

自引率

0.00%

发文量

期刊介绍： The Journal of Spectral Theory is devoted to the publication of research articles that focus on spectral theory and its many areas of application. Articles of all lengths including surveys of parts of the subject are very welcome. The following list includes several aspects of spectral theory and also fields which feature substantial applications of (or to) spectral theory. Schrödinger operators, scattering theory and resonances; eigenvalues: perturbation theory, asymptotics and inequalities; quantum graphs, graph Laplacians; pseudo-differential operators and semi-classical analysis; random matrix theory; the Anderson model and other random media; non-self-adjoint matrices and operators, including Toeplitz operators; spectral geometry, including manifolds and automorphic forms; linear and nonlinear differential operators, especially those arising in geometry and physics; orthogonal polynomials; inverse problems.